Esta dissertação apresenta um estudo sobre a construção de histórias em quadrinhos (HQs), inspiradas em contos do livro O Homem que Calculava, de Malba Tahan, e a exploração de conceitos matemáticos na leitura desses contos e na produção dessas histórias por alunos do Ensino Fundamental. Ela oferece uma contextualização das HQs desde sua origem, ressaltando seu surgimento e seu desenvolvimento no Brasil, além de sua presença na educação matemática escolar. Além disso, enfoca um grande autor e professor de Matemática brasileiro, apresentando sua trajetória e utilizando uma de suas obras como provocação à produção escrita discente. O estudo foi realizado na Escola Municipal de Ensino Fundamental Almirante Raphael Brusque, em Pelotas, RS, ao longo de 20 encontros semanais e envolveu uma turma de oitava série do Ensino Fundamental, cujos discentes residem na Colônia de Pescadores Z3. Em seu planejamento, definimos algumas etapas que reuniram atividades ligadas às áreas de Literatura, Matemática e Artes. Para a aplicação dessas atividades, desenvolvidas em sala de aula por três grupos, totalizando 13 alunos, consideramos a leitura de alguns contos narrados pelo personagem Beremiz, a interpretação dos correspondentes problemas matemáticos, e a criação de novas histórias e sua transformação em HQs, inspiradas nesses contos, que incluíram algumas características socioculturais da Colônia de Pescadores Z3. Durante o desenvolvimento das atividades, observamos o empenho e o progresso dos alunos na execução das diferentes tarefas que deram suporte a este estudo, que resultou na produção escrita discente de três livros de HQs. / This dissertation presents a study on the making of comic books inspired in some of the short stories of MalbaTahan’s The Man Who Counted and the exploration of mathematical concepts in the reading and production of these stories by elementary school students. It offers a contextualization of comic books from their origin, emphasizing their emergence and development in Brazil, besides their presence in school mathematics education. The dissertation also focuses on an important Brazilian author, writer and mathematics teacher, presenting his trajectory and using one of his works to instigate the written production of students. The study took place in the Almirante Raphael Brusque Elementary Education Municipal School, located in the city of Pelotas, RS, Brazil, during 20 weekly meetings and involved a class of eight graders who live in the Z3 fisher Colony. In its planning we defined some phases which brought together activities related to the fields of literature, mathematics and arts. Regarding the application of these activities in the classroom, which were developed by three groups adding up to 13 students, we considered the reading of some short stories narrated by the character Beremiz, the interpretation of their corresponding mathematical problems, and the creation of new stories, including their transformation to comic book format. The new stories were inspired in those stories and included some sociocultural characteristics of the Z3 fisher Colony. During the development of the activities we observed the commitment and the progress of the students while engaged in the several tasks that provided support for this study, which resulted in the written production of three comic books.

Orientador: Antonio Miguel / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-09T09:57:52Z (GMT). No. of bitstreams: 1 Vilela_DeniseSilva_D.pdf: 1524315 bytes, checksum: 9bbabd38825517fb6c7294587eeedc4c (MD5) Previous issue date: 2007 / Resumo: Como o termo matemática vem sendo usado na literatura acadêmica da Educação Matemática? Esta é a questão inicial que orienta este estudo investigativo realizado com base em publicações e pesquisas acadêmicas recentes em Educação Matemática. Com base nesses documentos, verificou-se a ocorrência, em freqüência significativa, de diversas adjetivações do termo matemática tais como: matemática escolar, matemática da rua, matemática acadêmica, matemática popular, matemática do cotidiano, etc. A partir da análise de alguns desses textos, constatou-se que as adjetivações, que ocorrem geralmente aos pares, apontam especificidades das matemáticas, tais como, diferenças em resultados, processos, valores, significados, conceitos, etc. A partir de uma visão de conjunto das especificidades apontadas nos textos pesquisados, as diversas adjetivações são interpretadas como jogos de linguagem que não possuiriam uma essência, mas apresentariam semelhanças de famílias, no sentido dado por Wittgenstein a este conceito. Para formular a questão acima, inspiramo-nos nos conceitos desse filósofo, bem como em sua concepção de filosofia, que possui uma perspectiva de ampliação dos significados alcançada mediante as descrições dos usos de um conceito, a qual possibilita dissolver a noção essencialista e referencial de significado A partir disso, para alcançar um sentido sociológico dessas adjetivações à interpretação filosófica é ampliada com conceitos da sociologia de Bourdieu, notadamente com o conceito de campo científico. As adjetivações expressariam uma tensão no campo das matemáticas: o reconhecimento da produção de conhecimentos matemáticos em diversas práticas que não só a dos matemáticos profissionais, mas também as dos professores, as de grupos profissionais, etc., e também o questionamento do monopólio da definição e atribuições do campo por matemáticos profissionais. Ou seja, as adjetivações são entendidas como objetivações de novos termos da gramática do campo das matemáticas. Além disso, são indicados elementos para uma compreensão das matemáticas como práticas sociais, não simplesmente como determinadas por estratégias racionais intencionais, e sim como práticas condicionadas pela própria estrutura da linguagem, que implica em regularidades as quais limitam e regulam as possibilidades de inteligibilidade e de desenvolvimento das matemáticas nas práticas especificas, mas que não constituem regulamentos que impediriam novos usos / Abstract: How used the term Mathematic in Mathematics Education literature has been? This is the main question that guides this investigation, supported by recent academic researches and publications in the field of Mathematics Education. Based on these writings, we have noticed the existence of several ways of adjetivizing the term mathematics such as: school mathematics, street mathematics, academic mathematics, popular mathematics, everyday mathematics, and so on. After analyzing some of these works, it can be seen that these adjectives, that often show up in pairs, point to mathematics specificities, such as difference in results, processes, values, meanings, concepts etc. From a global view of the specificities pointed in all researched texts, adjectives are understood as language-games that do not have an essence, but would present family resemblances, in the sense given by Wittgenstein to these concepts. To answer the question stated above, we were inspired by these Wittgenstein¿s concepts, as well as by his conception of philosophy, which has a tendency to broaden meanings through the use descriptions of a concept. This allows dissolving na essentialist notion of meaning as a last and universal reference. In order to search for a sociological sense for these adjectivize, our goal is to historically rescue this tendency to adjective in the current context of cultural studies in which modernity values are questioned. Thus, a philosophical explanation is broadened by concepts of Bourdieu's sociology, specially the concept of scientific field. The adjectives would express a struggle within the mathematics field, and the recognition that there is mathematical knowledge production in many practices beyond the professional mathematicians¿, like teachers¿, professional groups¿ etc. That is, adjectives are understood as objectivations for new terms of a grammar of mathematics fields. Besides, this work indicates elements for a understanding of mathematics as social practices, not merely determined by rational and intended strategies, but also as practices conditioned by language structures, which implies regularities that limit and adjust the possibilities of understanding and developmenting of mathematics within specific practices, but not representing regulations that could hinder new uses / Doutorado / Educação Matematica / Doutor em Educação

Este trabalho tem o objetivo de verificar como o logaritmo e a função logarítmica são abordados nos livros didáticos de Matemática do século XIX ao XXI, indicando a inserção desses conteúdos na Matemática Escolar brasileira. Baseamo-nos, dentre outros autores, em Choppin (2004), Valente (1999, 2004, 2005 e 2008) e Bittencourt (2004 e 2008) para identificarmos o livro didático como fonte de pesquisa da Matemática Escolar, a partir de suas formas conceituais, de enfoque didático ou referente à organização do saber. A fim de verificar relações entre o histórico dos logaritmos e da função logarítmica na Matemática e na Matemática Escolar, apresentamos a ideia dos logaritmos de Napier como facilitadores de cálculos, interpretamos sua definição geométrica por meio de um sistema de equações diferenciais ordinárias e, assim, mostramos um breve histórico sobre a inserção do logaritmo como função no Cálculo Integral. Os livros didáticos de Matemática analisados foram publicados entre os anos de 1879 e 2013. Nesta análise, consideramos o modo como os autores abordam ou tratam a Matemática, os tipos de atividades que são propostas, os tipos de explicações, definições, exemplos, gráficos, exercícios, aplicações e problemas associados aos logaritmos e à função logarítmica. Os resultados apontam que no século XIX os logaritmos eram tratados nos livros didáticos, quase sempre, por meio da Aritmética. A partir da década de 1890, eles são abordados, tanto no campo aritmético, pela associação à teoria das progressões, como no campo algébrico, sendo expoentes numa equação ou função. A partir da década de 1930 até os dias de hoje verificamos uma predominância da concepção algébrico-funcional dos logaritmos. Com base nas Orientações Curriculares para o Ensino Médio (2006), nos Parâmetros Curriculares Nacionais Ensino Médio (PCNs - 2000), nos Parâmetros Curriculares Nacionais+ Ensino Médio (PCNs+ Ensino Médio - 2002), no Exame Nacional do Ensino Médio e em livros didáticos recentes, verificamos que os logaritmos e a função logarítmica se inserem, atualmente, na Matemática Escolar brasileira, pela sua associação às aplicações, como por exemplo, juros compostos, dinâmica populacional, desintegração radioativa, potencial hidrogeniônico, Escala Richter, Escala de Magnitude de Momento (MMS) e nível de intensidade sonora. / This work aims to verify how the logarithm and logarithmic function are approached in the textbooks of Mathematics from the 19th to the 21st century, indicating the insertion of these contents in Brazilian School Mathematics. We are based, among other authors, in Choppin (2004), Valente (1999, 2004, 2005 and 2008) and Bittencourt (2004 and 2008) to identify the didactic book as a research source of School Mathematics, from its conceptual forms, of didactic approach or referring to the organization of knowledge. In order to verify relations between the logarithmic and logarithmic functions in Mathematics and School Mathematics, we present the idea of the logarithms of Napier as facilitators of calculations, we interpret their geometric definition by means of a system of ordinary differential equations and we show a brief history about the insertion of the logarithm as a function in the Integral Calculus. The mathematical textbooks analyzed were published between the years 1879 and 2013. In this analysis, we consider how authors approach or treat mathematics, the types of activities that are proposed, the types of explanations, definitions, examples, graphs, exercises, applications and problems associated with logarithms and logarithmic function. The results show that in the 19th century, logarithms were treated in textbooks, almost always, through Arithmetic. From the 1890s, they are approached, both in the arithmetic field, by association with the theory of progressions, and in the algebraic field, being exponents in an equation or function. From the 1930s to the present day we have found a predominance of the algebraic-functional conception of logarithms. Based on the Curriculum Guidelines for Secondary Education (2006), the National Curriculum Parameters - Secondary Education (PCN\'s - 2000), the National Curriculum Parameters + High School (PCN\'s + High School - 2002), the National High School Examination and textbooks recent, we have verified that the logarithms and the logarithmic function are currently inserted in Brazilian School Mathematics, by their association to the applications, such as compound interest, population dynamics, radioactive disintegration, hydrogen ionic potential, Richter Scale, Momentum Magnitude Scale (MMS) and level of sound intensity.

Orientador: Antonio Miguel / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-27T00:11:35Z (GMT). No. of bitstreams: 1 FerreiradeSantana_DianaPatricia_D.pdf: 61557598 bytes, checksum: d70e3e9305614149df56a017a6270c4c (MD5) Previous issue date: 2015 / Resumo: O objetivo deste trabalho é fazer uma leitura das idéias de Ludwig Wittgenstein sobre a linguagem, tendo o silêncio como fio condutor das nossas considerações. Temos uma dupla finalidade: a primeira é identificar as formas de silêncio na vida e obra do filósofo austríaco como uma tentativa de compreender o autor e seu estilo idiossincrático, marcado por uma escrita assistemática e aforística; a segunda é identificar as formas de silêncio expressos na aprendizagem da matemática escolar a partir da afirmação feita por Michael Peters de que há um potencial pedagógico na forma como o filósofo empreende sua crítica. Procuramos, através de uma perspectiva não convencional "mostrada" por Wittgenstein, identificar o não-dito, mostrá-lo e desvelar o feitiço por meio da linguagem que ainda prevalece na aprendizagem da matemática escolar / Abstract: The aim of this work is to make a reading of Ludwig Wittgenstein¿s ideas onlanguage taking the silence as thread of our considerations. We have a dual purpose: the first is to identify the forms of silence in the life and work of Austrian philosopher as an attempt to understand the author and his idiosyncratic style marked by an unsystematic and aphoristic writing; the second is to identify the forms of silence expressed in the learning of school mathematics from the assertion made by Michael Peters that there are pedagogical potential in how the philosopher makes his criticism. We seek, through unconventional perspective "shown" by Wittgenstein, identify the unspoken, show it and unveil the bewitchment by language that still prevails in the learning of school mathematics / Doutorado / Ensino e Práticas Culturais / Doutora em Educação

One of the main reasons that students struggle as they transition from arithmetic to algebra in the middle grades is that they fail to develop the appropriate understanding of the equal sign. Previous research has suggested that students need to move past an operational understanding and develop a relational understanding of the equal sign in order to work with algebraic equations successfully. Other research has suggested that the way that we interpret and utilize the equal sign is based on three main factors: multiple meanings of the equal sign, equation types, and structural conventions. This study extends both areas of research by analyzing two middle grade curricula and looking for what meanings, equation types, and structural conventions appear in both teacher and student materials. The study confirms that students are exposed to three main meanings of the equal sign in the middle grades. The study also describes which meanings of the equal sign are associated with particular equation types and the frequency with which these equation types appear throughout the 7th and 8th grade curricula. Study findings can be used to inform instruction, as they delineate the factors that are attended to while making sense of the equal sign in the middle grades.

Research shows that students who take advanced mathematics courses perform better on measures of college readiness than students who take less rigorous courses. However, no clear effect has been shown on requiring all students to take more advanced courses. This study examined whether increases in the number and level of mathematics courses required for high school graduation have resulted in increased levels of college aspirations and preparedness. Specifically, twenty years of data from a rural school district in Texas were analyzed to determine whether the impact on college entrance exam-taking and performance differed by the mathematics requirements in effect for each class. Logistic and linear regression modeling revealed no statistically significant effect of higher requirements. And while overall results by gender and race mirrored previous research, with males tending to have higher scores than females and White students tending to score higher than African-American and Latinx students, the increased requirements were not associated with any mitigation in these inequities.

Den här studien är en systematisk litteraturstudie som går ut på att presentera och analysera vad forskning visar beträffande svårigheter som elever möter inom området ”derivata” samt hur undervisningen kan utformas för att stötta eleverna i sitt lärande inom ”derivata”. Via systematiska sökningar som skedde både i databaser och manuellt valdes artiklar som passade in på urvalskriterier. Artiklarna analyserades utifrån frågeställningarna. Elevens svårigheter i sin förståelse för begreppet ”derivata” delades upp i tre huvudsakliga kategorier: tangentens ekvation och dess lutning i förhållande till ”derivata”, gränsvärde i förhållande till ”derivata” och förändringshastighet i förhållande till ”derivata”. Studien fann att eleverna uppvisade svårigheter när de gäller tangenten, tangentens lutning, förändringshastighet och gränsvärde. Att eleverna hade svårt med att förstå begreppet ”derivata” gjorde att de fick även svårare att se sambandet mellan alla andra begrepp. Gällande undervisningens utformning fann studien att användandet av olika representationer och digitala verktyg förebygger elevens svårigheter för begreppet ”derivata”. / This study is a systematic literature study aiming at presenting and analyzing what research shows regarding difficulties students encounter in the field of derivatives and how teaching can be designed to support students in their learning in derivatives. Through systematic searches which were done both in databases and manually, articles that matched given criteria were selected. The articles were analyzed based on the research questions. The students' difficulties in understanding the concept of derivatives were divided into three main categories: the tangent equation and its slope in relation to derivatives, the limit value in relation to derivatives and the rate of change in relation to derivatives. The study found that students experienced difficulties in the concept of the derivative, such as the tangent, the slope of the tangent, the rate of change and the limit. The fact that the students had difficulty with the concepts made them even more difficult to understand the connection between these concepts. Regarding the teaching, the study found that different representations and the using of digital tools prevent the students' difficulties in the concept of derivatives.

The South African education system is under a serious strain in relation to Mathematics attainment. Only 40% of learners in SA pass the final school leaving examination and only 5% of learners manage to pass Mathematics with more than 50%, according to The Economist (2014). In a bid to solve this problem the government proposes the use of ICTs (such as computer hardware and software, tablets, and smartphones) within teaching and learning. The assumption is ICTs can be utilised to address this important challenge and “facilitate ongoing improvement of educator skills” (The National Integrated ICT Policy White Paper: The White Paper, 2016: p.8). Research shows that teachers’ perceptions regarding the use of ICTs impact on their practices (Mwendwa, 2017; Munyengabe, Yiyi, He Haiyan, & Hitimana, 2017; Alharbi, 2012; Yuan & Chun-Yi Lee, 2012). This project intends to explore six grade 6 Mathematics teachers’ perceptions about whether and how pedagogy shifts with the use ICTs in the classrooms utilising Cultural Historical Activity Theory. This research utilises interviews as a method for the collection of empirical data to describe a group of research participants’ (or teachers’) perceptions who happen to be directly interviewed. These interviews have been conducted across two no-fee paying primary schools in the Western Cape Province (WCP), in South Africa (SA). Interviews were analysed along the CHAT dimensions: object, subject, tools, rules, community and division of labour to establish whether pedagogy altered along any of these dimensions. Findings indicate that teachers think pedagogy shifts in the ICT based lessons with division of labour becoming more fluid. Findings also show that the object of the activity system grows to encompass more than mere mathematical compression but also motivation, creativity and cognitive development. Besides, teachers stated that ICT based learning could assist learners in their mathematical attainment. This project is an investigation and not an intervention study. Recommendations are also suggested in this thesis for further research such as video-taping teaching and learning of mathematic contents and concepts in both traditional and computer-based classrooms. Further study in utilising classroom observations to focus on student-student interaction in relation to ICTs is also recommended.

This Diploma thesis is based on the teaching practice done online. It looks at the possibilities of online teaching of Mathematics and its concepts, and at how to teach Mathematics online well. The aim of the thesis is to compare distance learning in the Czech Republic and chosen countries in the European Union. The current situation changed in the European schooling and teaching was done remotely since Spring 2020. This thesis takes this situation and looks at three main areas: literature search, where theoretical background is described, summarized data for distance learning in the World, which I got from the internet, and lastly a part where I observed teaching in the given context, both as an observing student and as a teacher. The teaching practice was done in the first year of the lower secondary school, during a focus on the topic of solving equations. The analysis and the reflection of the class are put into the context with the analysis of the topic of solving equations as presented in chosen textbooks both at primary and lower secondary school level. The thesis also includes a summary of all the reports published during the pandemic by CSI that examined the impact of the pandemic on the teachers, the students, and the parents. The final part of the thesis presents a summary of gained...

During a year-long professional development, the faculty members at an elementary school received instruction on mathematics and how to use the Comprehensive Mathematics Instruction framework. The instruction and the framework were consistent with the standards suggested by the National Council of Teacher of Mathematics (2000). This thesis analyzes the mathematical language used by three fifth-grade teachers who participated in lesson study to create a research lesson based upon the Comprehensive Mathematics Instruction framework.